Control volume based finite difference method?
 

I don't like such a hybridization... i continue to distinguish finite volume and finite difference based on the starting gorverning equation. If you start from the integral form you will discretize in a FV manner, in the differential form in FD manner.

This apart any discussion on SM, FEM, etc.

thanx for the reply Prof. Denaro.
But that much I know. What I was looking for is a discussion on ' CONTROL VOLUME BASED FINITE DIFFERENCE METHOD'

Hi Medhi,

I do not understand well what is your question.
But what I could say is when you implement FV method, there is a moment when you have to specify the dot product between GRADIENT(phy) and the normal vector n to any faces of that control volume.
When the grid is orthogonal there is not any difficulty. But when the grid is not orthogonal, as in complex geometry, then this task is not trivial.

At the end you would need to express the first derivative of variable phy between two neighbouring nodes and located at the middle of the surface between these two nodes.
To achieve that you could use finite difference method and it is what you call "FV based FD"
Or in an alternative way, you could use shape functions like in Finite Element method and then you will use "FV based FE".

That's how I understant your question....:confused: